Solve x-10/x+9/1+frac{1{x+9}}

$$\frac { x - \frac { 10 } { x + 9 } } { 1 + \frac { 1 } { x + 9 } }$$

Evaluate

$$x-1$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x+9}{x+9}.

$$\frac{\frac{x\left(x+9\right)}{x+9}-\frac{10}{x+9}}{1+\frac{1}{x+9}}$$

Since \frac{x\left(x+9\right)}{x+9} and \frac{10}{x+9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x\left(x+9\right)-10}{x+9}}{1+\frac{1}{x+9}}$$

Do the multiplications in x\left(x+9\right)-10.

$$\frac{\frac{x^{2}+9x-10}{x+9}}{1+\frac{1}{x+9}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+9}{x+9}.

$$\frac{\frac{x^{2}+9x-10}{x+9}}{\frac{x+9}{x+9}+\frac{1}{x+9}}$$

Since \frac{x+9}{x+9} and \frac{1}{x+9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x^{2}+9x-10}{x+9}}{\frac{x+9+1}{x+9}}$$

Combine like terms in x+9+1.

$$\frac{\frac{x^{2}+9x-10}{x+9}}{\frac{x+10}{x+9}}$$

Divide \frac{x^{2}+9x-10}{x+9} by \frac{x+10}{x+9} by multiplying \frac{x^{2}+9x-10}{x+9} by the reciprocal of \frac{x+10}{x+9}.

$$\frac{\left(x^{2}+9x-10\right)\left(x+9\right)}{\left(x+9\right)\left(x+10\right)}$$

Cancel out x+9 in both numerator and denominator.

$$\frac{x^{2}+9x-10}{x+10}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-1\right)\left(x+10\right)}{x+10}$$

Cancel out x+10 in both numerator and denominator.

$$x-1$$

Expand

$$x-1$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x+9}{x+9}.

$$\frac{\frac{x\left(x+9\right)}{x+9}-\frac{10}{x+9}}{1+\frac{1}{x+9}}$$

Since \frac{x\left(x+9\right)}{x+9} and \frac{10}{x+9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x\left(x+9\right)-10}{x+9}}{1+\frac{1}{x+9}}$$

Do the multiplications in x\left(x+9\right)-10.

$$\frac{\frac{x^{2}+9x-10}{x+9}}{1+\frac{1}{x+9}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+9}{x+9}.

$$\frac{\frac{x^{2}+9x-10}{x+9}}{\frac{x+9}{x+9}+\frac{1}{x+9}}$$

Since \frac{x+9}{x+9} and \frac{1}{x+9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x^{2}+9x-10}{x+9}}{\frac{x+9+1}{x+9}}$$

Combine like terms in x+9+1.

$$\frac{\frac{x^{2}+9x-10}{x+9}}{\frac{x+10}{x+9}}$$

Divide \frac{x^{2}+9x-10}{x+9} by \frac{x+10}{x+9} by multiplying \frac{x^{2}+9x-10}{x+9} by the reciprocal of \frac{x+10}{x+9}.

$$\frac{\left(x^{2}+9x-10\right)\left(x+9\right)}{\left(x+9\right)\left(x+10\right)}$$

Cancel out x+9 in both numerator and denominator.

$$\frac{x^{2}+9x-10}{x+10}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-1\right)\left(x+10\right)}{x+10}$$

Cancel out x+10 in both numerator and denominator.

$$x-1$$